We review some known dynamical models of epidemics, given by coupled systems of di¤erential equations, and propose a simple SI-type model of HIV-transmision that accounts for population growth. It allows exact analysis of solution and makes speci…c predictions on the spread of HIV and its e¤ect on populations. Then we outline an extended version of the model based on several behavioral/gender g...

This paper develops a two-regional growth model with amenity, capital accumulation and regional public goods with public goods and fiscal policies. The economy consists of two regions and each region consists of the industrial sector and public sector. The industrial sector provides goods in perfectly competitive markets. The public sector, which is financed by the regional government’s tax inc...

The asteroid belt helps us in reconstructing the origin and the evolution of the solar system, probably better than the planets themselves. This is because the asteroid belt provides several key constraints that can be used to effectively guide the development, calibration, and validation of evolutionary models. Compared to other small-body populations, such as the Kuiper belt or Oort cloud, th...

Let F : M → M be a continuous dissipative map of a separable metric space M . Consider a finite collection A of closed F -forward invariant sets that is closed under intersection and that contains M . For all ! > 0, let X be a Markov chain for which the elements of A are absorbing (e.g., extinction boundaries for a population, genotype, or strategy) and such that d(X t+1, F (X ! t )) ≤ ! for al...

In a standard bifurcation of a dynamical system, the stationary points (or more generally attractors) change qualitatively when varying a control parameter. Here we describe a novel unusual effect, when the change of a parameter, e.g. a growth rate, does not influence the stationary states, but nevertheless leads to a qualitative change of dynamics. For instance, such a dynamic transition can b...